From a certain number of people who attended an interview

Question

From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?

A. 2
B. 4
C. 6
D. 8
E. Cannot be determined

A. 2
B. 4
C. 6
D. 8
E. Cannot be determined

fameatop · Answer

nCx = nC(x+2) -----(Eq1)

or in other words, 
x + x + 2 = n
2x+2 = n -----(Eq2)
So logically x can take any value as long as it satisfies both the equations.

X N
2 6
4 10
6 14
8 18

For all the above mentioned values of X & N both of the equations are satisfied. 
So, answer should be E & not C.

Sravan, can you kindly confirm the OA once again.

SVaidyaraman · Answer

Yes you are right. I was about to edit the question. Kindly take a look at it now.

SVaidyaraman · Answer

fameatop,

I guess you have not seen the question after I edited it. Your comment needs to be removed as the OA is A and not E.

nitin6305 · Answer

Can you please provide an explanation for the OA?

SVaidyaraman · Answer

Solution:

1. We are selecting from the same number of people when x as well as x+2 selections are made and the number of selections that can be made is the same. i.e., nCx = nC(x+2) 
i.e., x + (x+2) =n or 
n=2x+2

2. The other information we have is that at least 2 interviews were conducted per day and the interviews were completed in 4 days. That is n has to be at least 2*4 = 8.

3. Now plug in the values of x from the answer choices. If x=2, n=6. This is not possible because it is less than 8. Other values are possible because n>8 in all those cases.

Asifpirlo · Answer

solution:
At least 2 interviews a day, so minimum 8 interviews in four days. Thus at least a total of 8 candidates should be there.

Let, total candidates = n
according to the question,
 nCx = nC(x+2) 
or, nCn-x = nCx+2  
or, n-x = x+2
so, n = 2x+2

Remember total least number should be 8? So below 8 we can't expect anything.
Put x=2, then n=6 that is unacceptable.
so x is not equal to 2 . Answer: A

obelix_asterix · Answer

I am lost - how de we get x + (x+2) =n? I am getting a second order equation.

Regor60 · Answer

The number of ways to select X people from N attendees is

N!/X!(N-X)!

We're told that at least 2 people are interviewed per day and that the interviews take 4 days, so N>=8

The number of ways to select X+2 people from N attendees is

N!/(X+2)!(N-X-2)!

We're told the number of ways are equal:

N!/X!(N-X)! = N!/(X+2)!(N-X-2)!, so

(X+2)!(N-X-2)! = X!(N-X)! so

(X+1)(X+2) = (N-X)(N-X-1)

Multiplying out and collecting terms yields:

N^2-2X(N+1)-N-2 = 0

Substituting X=2 as the first potential answer yields:

N^2-5N-6 = 0 or

(N-6)(N+1) = 0 or

N=6

Since N=6 fails to meet the minimum of 8, A is the correct answer

Posted from my mobile device

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From a certain number of people who attended an interview

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From a certain number of people who attended an interview

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